Portable dynamic notebook
ManipulatePlot[Sin[a x + b], {x, 0, 6}, {a, 1, 4, 0.5}, {b, 0, 10, 0.5}]
Manipulate[
Plot[Evaluate[
y[t] /. First[
NDSolve[ {y''[x] == -x y[x], y[0] == a, y'[0] == b},
y, {x, 0, 4}]]], {t, 0, 4},
Epilog -> {Point[{4, 1/2}], Green, Arrow[{{0, a}, {1, b + a}}], Red,
Point[{0, a}]}, ImagePadding -> 25, PlotRange -> {{0,4.5}, {-3,3}}],
{{a, 1}, -3, 3, 0.5},
{{b, 0}, -3, 3, 0.5}]